Question

For an upcoming event a 2500 seat arena is selling tickets for $25 and $15. At least 1000 tickets

must be priced at $15 and total sales need to exceed $10,000 to make a profit. Let x represent the
number of tickets priced at $25 and y represent the number of tickets priced at $15.

Answer 1

It is assumed you are looking for the inequalities that the problem dictates.

Given

• Number of $25 tickets = x, total of $25 tickets is 25x.
• Number of $15 tickets = y., total of $15 tickets is 15y.

Conditions

Number of seats is at most 2500:

• x + y ≤ 2500

At least 1000 tickets must be priced at $15:

• y ≥ 1000

Total sales need to exceed $10,000:

• 25x + 15y ≥ 10000

So there is a system of 3 inequalities you need to solve.

Let me know if you need additional guidance on solving the system.